Population Genetics

1
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
2
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00






3
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.8 0.2





4
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.8 0.2
Relative Fitness 1 1 0.25




5
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.8 0.2
Relative Fitness 1 1 0.25
Survival to Reproduction 0.16 0.48 0.09



6
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.8 0.2
Relative Fitness 1 1 0.25
Survival to Reproduction 0.16 0.48 0.09 0.73



7
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.8 0.2
Relative Fitness 1 1 0.25
Survival to Reproduction 0.16 0.48 0.09 0.73
Geno. Freq., breeders 0.22 0.66 0.12 1.00


8
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.8 0.2
Relative Fitness 1 1 0.25
Survival to Reproduction 0.16 0.48 0.09 0.73
Geno. Freq., breeders 0.22 0.66 0.12 1.00
Gene Freq's, gene pool p 0.55 q 0.45

9
Population Genetics I. Basic Principles II.
X-linked Genes III. Modeling Selection A.
Selection for a Dominant Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.8 0.2
Relative Fitness 1 1 0.25
Survival to Reproduction 0.16 0.48 0.09 0.73
Geno. Freq., breeders 0.22 0.66 0.12 1.00
Gene Freq's, gene pool p 0.55 q 0.45
Genotypes, F1 0.3025 0.495 0.2025 100
10
III. Modeling Selection A. Selection for a
Dominant Allele ?p spq2/1-sq2
11
III. Modeling Selection A. Selection for a
Dominant Allele ?p spq2/1-sq2 - in our
previous example, s .75, p 0.4, q 0.6
12
III. Modeling Selection A. Selection for a
Dominant Allele ?p spq2/1-sq2 - in our
previous example, s .75, p 0.4, q 0.6 -
?p (.75)(.4)(.36)/1-(.75)(.36) . 108/.73
0.15
13
III. Modeling Selection A. Selection for a
Dominant Allele ?p spq2/1-sq2 - in our
previous example, s .75, p 0.4, q 0.6 -
?p (.75)(.4)(.36)/1-(.75)(.36) . 108/.73
0.15 p0 0.4, so p1 0.55 (check)
14
III. Modeling Selection A. Selection for a
Dominant Allele ?p spq2/1-sq2
15
III. Modeling Selection A. Selection for a
Dominant Allele ?p spq2/1-sq2 - next
generation (.75)(.55)(.2025)/1 - (.75)(.2025) -
0.084/0.85 0.1
16
III. Modeling Selection A. Selection for a
Dominant Allele ?p spq2/1-sq2 - next
generation (.75)(.55)(.2025)/1 - (.75)(.2025) -
0.084/0.85 0.1 - so
17
III. Modeling Selection A. Selection for a
Dominant Allele ?p spq2/1-sq2 - next
generation (.75)(.55)(.2025)/1 - (.75)(.2025) -
0.084/0.85 0.1 - so p0 to p1 0.15
p1 to p2 0.1
18
III. Modeling Selection A. Selection for a
Dominant Allele so, ?p declines with each
generation.
19
III. Modeling Selection A. Selection for a
Dominant Allele so, ?p declines with each
generation. BECAUSE as q declines, a greater
proportion of q alleles are present in
heterozygotes (and invisible to selection). As q
declines, q2 declines more rapidly...
20
III. Modeling Selection A. Selection for a
Dominant Allele so, ?p declines with each
generation. BECAUSE as q declines, a greater
proportion of q alleles are present in
heterozygotes (and invisible to selection). As q
declines, q2 declines more rapidly... So, in
large populations, it is hard for selection to
completely eliminate a deleterious
allele....
21
III. Modeling Selection A. Selection for a
Dominant Allele B. Selection for an
Incompletely Dominant Allele
22
B. Selection for an Incompletely Dominant
Allele
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.2
Relative Fitness 1 0.5 0.25
Survival to Reproduction 0.16 0.24 0.09 0.49
Geno. Freq., breeders 0.33 0..50 0.17 1.00
Gene Freq's, gene pool p 0.58 q 0.42
Genotypes, F1 0.34 0..48 0.18 100
23
B. Selection for an Incompletely Dominant
Allele - deleterious alleles can no longer
hide in the heterozygote its presence always
causes a reduction in fitness, and so it can be
eliminated from a population.
24
III. Modeling Selection A. Selection for a
Dominant Allele B. Selection for an
Incompletely Dominant Allele C. Selection
that Maintains Variation
25
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.4 0.8 0.2
Relative Fitness 0.5 (1-s) 1 0.25 (1-t)
Survival to Reproduction 0.08 0.48 0.09 0.65
Geno. Freq., breeders 0.12 0.74 0.14 1.00
Gene Freq's, gene pool p 0.49 q 0.51
Genotypes, F1 0.24 0.50 0.26 100
26
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of
27
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p)
28
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p) 2) rate at which these AA are lost
(s).
29
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p) 2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele ps
30
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p) 2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele ps -
Likewise the probability of losing an 'a'
qt
31
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
Consider an 'A" allele. It's probability of
being lost from the population is a function
of 1) probability it meets another 'A'
(p) 2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele ps -
Likewise the probability of losing an 'a' qt
- An equilibrium will occur, when the
probability of losing A an a are equal when ps
qt.
32
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
An equilibrium will occur, when the probability
of losing A an a are equal when ps qt.
33
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
An equilibrium will occur, when the probability
of losing A an a are equal when ps qt. -
substituting (1-p) for q, ps (1-p)t ps t
- pt ps pt t p(s t) t peq
t/(s t)
34
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
An equilibrium will occur, when the probability
of losing A an a are equal when ps qt. -
substituting (1-p) for q, ps (1-p)t ps t
- pt ps pt t p(s t) t peq
t/(s t) - So, for our example, t 0.75, s
0.5 - so, peq .75/1.25 0.6
35
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
so, peq .75/1.25 0.6
p 0.6, q 0.4 AA Aa aa
Parental "zygotes" 0.36 0.48 0.16 1.00
prob. of survival (fitness) 0.4 0.8 0.2
Relative Fitness 0.5 (1-s) 1 0.25 (1-t)
Survival to Reproduction 0.18 0.48 0.04 0.70
Geno. Freq., breeders 0.26 0.68 0.06 1.00
Gene Freq's, gene pool p 0.6 q 0.4 CHECK
Genotypes, F1 0.36 0.48 0.16 100
36
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
so, peq .75/1.25 0.6 - so, if p gt 0.6, it
should decline to this peq
p 0.7, q 0.3 AA Aa aa
Parental "zygotes" 0.49 0.42 0.09 1.00
prob. of survival (fitness) 0.4 0.8 0.2
Relative Fitness 0.5 (1-s) 1 0.25 (1-t)
Survival to Reproduction 0.25 0.48 0.02 0.75
Geno. Freq., breeders 0.33 0.64 0.03 1.00
Gene Freq's, gene pool p 0.65 q 0.35 CHECK
Genotypes, F1 0.42 0.46 0.12 100
37
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote -
so, peq .75/1.25 0.6 - so, if p gt 0.6, it
should decline to this peq
0.6
38
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism -
39
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism - - equilibrium
can occur if AA and aa are each fit in a given
niche, within the population. The equilibrium
will depend on the relative frequencies of the
niches and the selection differentials...
40
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism - - equilibrium
can occur if AA and aa are each fit in a given
niche, within the population. The equilibrium
will depend on the relative frequencies of the
niches and the selection differentials... -
can you think of an example??
41
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism - - equilibrium
can occur if AA and aa are each fit in a given
niche, within the population. The equilibrium
will depend on the relative frequencies of the
niches and the selection differentials... -
can you think of an example?? Papilio
butterflies... females mimic different models and
an equilibrium is maintained in fact, an
equilibrium at each locus, which are also
maintained in linkage disequilibrium.
42
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection
43
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection - the fitness depends on
the frequency...
44
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection - the fitness depends on
the frequency... - as a gene becomes rare, it
becomes advantageous and is maintained in the
population...
45
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection - the fitness depends on
the frequency... - as a gene becomes rare, it
becomes advantageous and is maintained in the
population... - "Rare mate"
phenomenon...
46
- Morphs of Heliconius melpomene and H.
erato Mullerian complex between two distasteful
species... positive frequency dependence in both
populations to look like the most abundant
morph
47
C. Selection that Maintains Variation 1.
Heterosis - selection for the heterozygote 2.
Multiple Niche Polymorphism 3. Frequency
Dependent Selection 4. Selection Against the
Heterozygote
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
48
4. Selection Against the Heterozygote
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
49
4. Selection Against the Heterozygote - peq
t/(s t)
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
50
4. Selection Against the Heterozygote - peq
t/(s t) - here .25/(.50 .25) .33
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
51
4. Selection Against the Heterozygote - peq
t/(s t) - here .25/(.50 .25) .33 -
if p gt 0.33, then it will keep increasing to
fixation.
p 0.4, q 0.6 AA Aa aa
Parental "zygotes" 0.16 0.48 0.36 1.00
prob. of survival (fitness) 0.8 0.4 0.6
Relative Fitness 1 0.5 0.75
Corrected Fitness 1 0.5 1.0 1 0.25
formulae 1 s 1 t
52
4. Selection Against the Heterozygote - peq
t/(s t) - here .25/(.50 .25) .33 -
if p gt 0.33, then it will keep increasing to
fixation. - However, if p lt 0.33, then p will
decline to zero... AND THERE WILL BE FIXATION FOR
A SUBOPTIMAL ALLELE....'a'... !! UNSTABLE
EQUILIBRIUM!!!!